Mathematical Thinking DPF
20 patterns · 486 sections
Choose a heading to read that text in full, or open the complete publication.
Table of contents
In the published reading order. Pattern IDs are stable references, not sequence numbers.
- Table of Contents
Mathematical Thinking DPF Architectural Reference
- MATH.Reference:1 - Problem frame - Construct mathematics for the question
- MATH.Reference:2 - Problem and forces - Make a usable construction
MATH.Reference:3 - Solution - Connect constructions through what they supply
- MATH.Reference:3.1 - Form objects, operations and representations
- MATH.Reference:3.2 - Obtain an argument and the object it supports
- MATH.Reference:3.3 - Change a construction and develop its theory
- MATH.Reference:3.4 - Return a construction to further work
- MATH.Reference:3.5 - Use this contribution within the wider repertoire
- MATH.Reference:3.6 - Constituent actions in ongoing work
- MATH.Reference:4 - Worked use - Choose a representation after the question changes
- MATH.Reference:5 - Worked use - Construct a choice after finding an obstruction
- MATH.Reference:6 - Checks and common failures - Preserve what the next construction needs
- MATH.Reference:7 - Consequences, biases and limits
- MATH.Reference:8 - Architectural Rationale - Organize by reusable constructions
- MATH.Reference:9 - Source use and currentness
- MATH.Reference:10 - Relations to further reasoning and work
- MATH.Reference:End
Part A - Choose and relate constructions
- MATH.16 - Choose a Mathematical Construction from Its Required Maps (Universal Property)
- MATH.17 - Construct Mathematical Spaces of Operations and Operations on Them
- MATH.1 - Build a Mathematical Structure of Composable Paths
- MATH.2 - Treat Objects as the Same While Preserving Operations (Quotient)
- MATH.5 - Extend a Generator Assignment While Preserving Operations (Homomorphism)
- MATH.7 - Transport a Mathematical Structure Through a Bijection
- MATH.18 - Compare Mathematical Accounts through Interpretations
Part C - Change a construction and develop its theory
- MATH.11 - Construct an Invariant from Transformation Rules
- MATH.13 - Derive a Consequence from a Symmetry
- MATH.8 - Generate a Solution Family by Symmetry
- MATH.9 - Determine Whether and How a Choice Rule Can Respect Symmetry
- MATH.10 - Improve a Mathematical Candidate or Derive a Necessary Condition by Admissible Variation
- MATH.21 - Construct an Object through Convergent Approximations
- MATH.22 - Change Axioms and Trace Their Consequences
- MATH.23 - Develop a Conjecture by Changing a Construction